Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

Americans pronounce vague as VAYG (/veɪg/). You'll hear it in sentences like "A vague figure guided the group again" or "She gave a vague answer when we questioned her" — more examples below.
Record yourself saying "vague" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 3 sounds. Explore each sound's mouth shape and how it's made.
Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher toward the roof of the mouth.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "vague", the "g" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.